B. Number · Operations: Exponents, Factors, Fractions, Decimals, Integers, Percents and Proportions

Increasing and Decreasing by a Percent in Your Head

B2.3 B2.2 A1About 45 minutes

Learning goals

I can increase or decrease a whole number by 1%, 5%, 10%, 25%, 50% and 100% using mental math.
I can explain the strategy I used.
I can solve sale-price and growth problems with percents.

Words to know

increase
To make larger. Increasing 80 by 25% means adding 25% of 80 to 80.

decrease
To make smaller. Decreasing 80 by 25% means subtracting 25% of 80 from 80.

discount
The amount taken off a price.

sale price
The price after the discount is subtracted.

Remember from Grade 6

In Grade 6 you found 1%, 5%, 10%, 15%, 25% and 50% of a number in your head, and you found sale prices and sales tax. In Grade 7 you will increase and decrease numbers by a percent, including by 100%, and explain your strategy out loud.

Let's start with registration fees

Last year, registration for a youth hockey league cost $200. This year it went up by 5%. What is the new fee?

10% of 200 is 20. 5% is half of that: 10.
Increase: 200 + 10 = $210.

That is a two-step strategy: find the percent, then add it (or subtract it for a decrease).

A 5% increase adds a small piece to the whole bar: $200 + $10 = $210, which is 105% of last year's fee.

Two strategies

Strategy 1: Find the part, then add or subtract.

Increase 80 by 25%: 25% of 80 = 20. 80 + 20 = 100.
Decrease 80 by 25%: 80 − 20 = 60.

Strategy 2: One step with a fraction.

Decrease by 25% → you keep 75% = 3/4. 3/4 of 80 = 60.
Increase by 25% → you end with 125% = 5/4. 80 ÷ 4 × 5 = 100.
Increase by 50% → 1 1/2 times. Decrease by 50% → half.
Increase by 100% → double it. Decrease by 100% → 0 (nothing is left).

Think of 80 as four quarters of 20. A 25% decrease removes one quarter (60). A 25% increase adds one more quarter (100).

Change	Quick way to find the part	Example with 240
1%	Divide by 100	Increase: 240 + 2.4 = 242.4
5%	Half of 10%	Decrease: 240 − 12 = 228
10%	Divide by 10	Increase: 240 + 24 = 264
25%	Divide by 4 (half of half)	Decrease: 240 − 60 = 180
50%	Divide by 2	Increase: 240 + 120 = 360
100%	The whole number itself	Increase: 240 + 240 = 480. Decrease: 240 − 240 = 0

Mental math strategies for increasing and decreasing 240.

Worked example

Example 1: Sale price

A winter jacket costs $96. It is on sale for 25% off. What is the sale price?

25% is 1/4. 96 ÷ 4 = 24. The discount is $24.
96 − 24 = 72.
Check with Strategy 2: you pay 3/4 of 96. 24 × 3 = 72. ✓

$72

Worked example

Example 2: Growth

A town has 3 200 people. Its population increases by 5%. What is the new population?

10% of 3 200 = 320.
5% is half of 10%: 160.
3 200 + 160 = 3 360.

3 360 people

Worked example

Example 3: 1% and 100%

Increase 600 by 1%. Then increase 75 by 100%.

1% of 600 = 600 ÷ 100 = 6. 600 + 6 = 606.
100% of 75 is 75. 75 + 75 = 150. (Increasing by 100% doubles a number.)

606 and 150

Explain your strategy

When you explain, say three things: what percent you found first, how you found it, and whether you added or subtracted. For example: "10% of 60 is 6, so 5% is 3. It's a decrease, so 60 − 3 = 57." Then ask yourself: should the answer be bigger or smaller than the start?

Hands-on activity

Flyer price changes

You need: a store flyer (paper or online) and paper and a pencil.

Choose 6 items with prices you can round to whole dollars.
For each item, find the price after a 25% off sale, a 10% off sale and a 50% off sale. Do it in your head, then write the answer.
Pretend that prices go up by 5% next year. Find each new price.
Explain one of your strategies to a grown-up, using the three-part explanation from the tip.

What to look for: e.g. a $40 item → 25% off: $30; 10% off: $36; 50% off: $20; up 5%: $42.

Math talk: "Which percent change was the easiest to do in your head? Why?"

Just for fun

If the number of socks in your drawer increases by 100%, you don't get more matching pairs. You just get twice as many lonely socks.

Your turn

Increase 60 by 10%.

Decrease 60 by 10%.

Increase 40 by 25%.

Decrease 200 by 5%.

Increase 300 by 1%.

Increase 75 by 100%.

Decrease 90 by 50%.

More practice: warm-up

What is 10% of 50?

Increase 50 by 50%.

Decrease 80 by 25%.

Increase 12 by 100%.

Decrease 400 by 1%.

More practice: on your own

A $96 pair of skates is 25% off. What is the sale price? Explain your strategy.

A concert ticket was $40. The price goes up by 5%. What is the new price?

A town of 3 200 people grows by 10%. What is the new population?

Decrease 700 by 1% and then, separately, decrease 700 by 10%.

A video-game score of 64 is increased by 50%. Then the new score is increased by 25%. What is the final score?

Challenge

Increase 80 by 10%. Then decrease the answer by 10%. Do you get back to 80? Explain.

A price goes from $60 to $75. By what percent did it increase?

A store says, "Everything is 100% off!" What would you pay for a $35 item? Why do stores almost never say this?

Check your understanding

Quiz

Increase 80 by 25%.

Decrease 500 by 5%.

What happens when you increase a number by 100%?

A $48 game is 50% off. What is the sale price?

Increase 900 by 1%.

Which is the same as decreasing a number by 25%?

For parents and teachers

Big idea: The Ontario curriculum (B2.3) asks Grade 7 students to use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50% and 100%, and explain the strategies used. Explaining is part of the expectation, so ask your child to talk through each one.

Common difficulties:

Giving the percent instead of the new amount (answering 20 when asked to increase 80 by 25%).
Thinking an increase and a decrease by the same percent cancel out.
Dividing by 5 to find 5% (5% is half of 10%, which is dividing by 20).

How to help: Use flyers and sale signs. Ask, "What will we actually pay?" and "How did you figure that out?" This lesson builds A1 skills: explaining reasoning, choosing efficient strategies and connecting math to money decisions.